Momentum
In classical mechanics, linear momentum or translational momentum (pl. momenta; SI unit kg m/s, or equivalently, N s) is the product of the mass and velocity of an object. For example, a heavy truck moving rapidly has a large momentum—it takes a large or prolonged force to get the truck up to this speed, and it takes a large or prolonged force to bring it to a stop afterwards. If the truck were lighter, or moving more slowly, then it would have less momentum. Tossup Questions # In quantum mechanics, the Fourier transform of this quantity's operator is represented by the position operator, and this quantity's operator is equal to negative i times h bar times the gradient. Translation invariance of the Hamiltonian or Lagrangian implies conservation of this quantity, which is equal to the product of h bar and the wave number for a photon. It is conserved in both elastic and inelastic collisions, and its change in a given time interval is the impulse. Its time derivative is equal to the product of mass and acceleration by Newton's Second Law. For 10 points, identify this product of mass and velocity. # A controversy exists over the calculation of this quantity for electromagnetic waves in dielectrics between equations proposed by Minkowski and by Abraham; Barnett suggests that one equation gives the kinetic and the other gives the canonical form of this quantity. This quantity is always equal to the Planck constant over an object's (*) de Broglie wavelength. Special relativity sets the square of energy equal to c to the fourth times invariant mass squared plus c squared times this quantity squared. This quantity is conserved in all closed system collisions, whether elastic or inelastic. For 10 points, name this quantity, equal to the product of mass and velocity. # The cross product of this quantity's vector with the L vector, minus "mass times k times r-hat," gives the Laplace- Runge-Lenz vector. One law governing this quantity is a consequence of the Lagrangian's translational invariance. The time rate of change in this quantity is equal to a particle's net force according to Newton's second law. Taking Planck's constant over this quantity gives a particle's de Broglie wavelength. Like all closed systems, both inelastic and elastic collisions conserve this quantity. For 10 points, name this quantity that equals mass times velocity. # The quantum mechanical operator for this quantity is negative i times h-bar times the gradient, and Planck's constant divided by this quantity gives the De Broglie wavelength. By Newton's second law, force is the time derivative of this quantity, whose change is known as the impulse. Unlike kinetic energy, it is conserved in inelastic collisions, and it is usually symbolized "p." For 10 points, name this quantity, the product of the mass and velocity of a moving body. # In quantum mechanics, this property is given by Dirac's constant over i times the gradient, and it's not position, but a discredited thought experiment that predicts the future through present knowledge of it everywhere is called Laplace's demon. In relativistic physics, this quantity's formula includes the rest mass and the * Lorentz factor. This property and kinetic energy are conserved in elastic collisions, and this quantity's change is known as impulse while its time derivative is force. For 10 points, name this measure symbolized p, defined as an object's mass times its velocity. # In quantum mechanics, this quantity for a photon is given by h-bar times the wave vector k, while its operator is given by h-bar divided by i, times the gradient. When light passes through a slit, the uncertainty in the vertical component of this quantity is given by its horizontal component times wavelength over slit width. The kinetic energy of a particle can be stated as this quantity squared over twice its mass. Because the traditional statement for Newton's second law does not account for changes in mass, that law is better stated as force equals the time derivative of this quantity. For 10 points, name this conserved quantity denoted p, equal to the product of mass and velocity. # Noether's theorem implies that because of space translation symmetry, this quantity is conserved. In relativity, a massless particle's energy is equal to this multiplied by the speed of light. This quantity can also be found by dividing Planck's constant by the de Broglie wavelength. At non-relativistic speeds, this quantity squared divided by two times the mass gives the kinetic energy. The change in this quantity is called the (*) impulse. Newton's second law states that force is proportional to the time derivative of this quantity. For 10 points, name this quantity that can be found as the product of mass and velocity and is often denoted p. # Free-particle solutions to the Schrodinger equation are eigenstates of this quantity's namesake operator. For massless objects, this quantity is equal to the energy over the speed of light. The change in this quantity is known as impulse, and it is conserved in both inelastic and elastic collisions. The original formulation of Newton's Second Law states that its first derivative is equal to force. For 10 points, identify this product of mass and velocity, denoted p. # The conservation of this quantity is due to the translational invariance of the Lagrangian, according to Noether's theorem. The De Broglie wavelength of a particle is equal to Planck's constant divided by this quantity for the particle. Heisenberg's Uncertainty Principle was originally given in terms of errors in position and this quantity. This quantity is conserved in both inelastic and elastic collisions, and the change in this quantity is equal to force times time, also known as impulse. For 10 points, name this quantity symbolized p, equal to mass times velocity.